A Rosenzweig-MacArthur (1963) Criterion for the Chemostat. (18th July 2016)

• Record Type: Journal Article
• Authors: Lindström, Torsten; Cheng, Yuanji
• Other Names: Candan Tuncay Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2016(2016)
• Publication Date: 2016-07-18
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2016/5626980
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : The Rosenzweig-MacArthur (1963) criterion is a graphical criterion that has been widely used for elucidating the local stability properties of the Gause (1934) type predator-prey systems. It has not been stated whether a similar criterion holds for models with explicit resource dynamics (Kooi et al. (1998)), like the chemostat model. In this paper we use the implicit function theorem and implicit derivatives for proving that a similar graphical criterion holds under chemostat conditions, too.